Global existence and decay of solutions to the Fokker-Planck-Boltzmann equation

Linjie Xiong; Tao Wang; Lusheng Wang

doi:10.3934/krm.2014.7.169

Article Contents

2014, Volume 7, Issue 1: 169-194. Doi: 10.3934/krm.2014.7.169

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Global existence and decay of solutions to the Fokker-Planck-Boltzmann equation

1.
School of Mathematics and Statistics, Wuhan University, Wuhan 430072

Received: May 31, 2013

Revised: September 30, 2013

Published: February 2014

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Abstract

The Cauchy problem to the Fokker-Planck-Boltzmann equation under Grad's angular cut-off assumption is investigated. When the initial data is a small perturbation of an equilibrium state, global existence and optimal temporal decay estimates of classical solutions are established. Our analysis is based on the coercivity of the Fokker-Planck operator and an elementary weighted energy method.

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Mathematics Subject Classification: Primary: 35Q20; Secondary: 82C31, 76P05, 83C40.

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